I'll answer my own question.
There is a huge jump in 'score' just for using a key phrase an arbitrary five times.
Another large jump for using a key phrase at the beginning of the body.
And another for using it in your title.
Doing the above gets you 70% SEO rating, even if the text makes no sense. The rating doesn't take into consideration quality aspects like grammar, humour, link-baiting, helpfulness, usefulness, etc. Randomly adding a few more keywords from the list takes it up to 96%. If you miss your intended 'readability grade level', it only affects the score a little.
You'd be better off with a simple checklist, as a high score could give you a false sense of security about your writing.
The keyword tool is quite neat, but it's just as easy to use GWT in the same way.